Find the value of each determinant

Solution :

a).

The different three letter initials that people have is :

= 26 x 26 x 26

= [tex]26^3[/tex]

= [tex]17576[/tex]

b). The first place to be fill in26 ways.

The second place to be filled in 25 ways

The third place to be filled in 24 ways.

Therefore, total number of three letter initial with no repetition is :

= 26 x 25 x 24

= [tex]15600[/tex]

c). The total number of three letter initial begin with X = 1 x 26 x 26

                                                                                          = [tex]676[/tex]

d). The total number of the three letter initials that begin with letter 'F' an end with letter 'D' is = 1 x 26 x 1

                                 = [tex]26[/tex]

Answer:

The right answer is:

(a) 0.1456

(b) 18.125, 69.1202, 8.3139

Step-by-step explanation:

Given:

N = 24

n = 5

r = 7

The improperly drilled gearboxes "X".

then,

⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]

(a)

P (all gearboxes fit properly) = [tex]P(x=0)[/tex]

                                               = [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]

                                               = [tex]0.1456[/tex]

(b)

According to the question,

[tex]X = 91+5[/tex]

Mean will be:

⇒ [tex]\mu = E(x)[/tex]

       [tex]=E(91+5)[/tex]

       [tex]=9E(1)+5[/tex]

       [tex]=9.\frac{nr}{N}+5[/tex]

       [tex]=9.\frac{5.7}{24} +5[/tex]

       [tex]=18.125[/tex]

Variance will be:

⇒ [tex]\sigma^2=Var(X)[/tex]

         [tex]=V(9Y+5)[/tex]

         [tex]=81.V(Y)[/tex]

         [tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]

         [tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]

         [tex]=69.1202[/tex]

Standard deviation will be:

⇒ [tex]\sigma = \sqrt{69.1202}[/tex]

       [tex]=8.3139[/tex]      

Answer:

(0.3478, 0.5522)

Step-by-step explanation:

Given:

Total number of red marbles, x = 45

Total number of marbles, n = 100

Phat = x / n = 45 / 100 = 0.45

The confidence interval, C.I is given by :

Phat ± Zcritical * standard error

Phat ± Zcritical * √Phat(1 - Phat) / n

Zcritical at 96% = 2.0537

The standard error = √Phat(1 - Phat) / n

S.E = √(0.45 * 0.55) / 100 = 0.0497493

C.I = 0.45 ± (2.0537 * 0.0497493)

C.I = 0.45 ± 0.10217013741

C. I = (0.3478, 0.5522)

9514 1404 393

Answer:

  yes

Step-by-step explanation:

No x-value is repeated, so these ordered pairs do represent a function.

Answer:

1

Use the quadratic formula

=

−

±

2

−

4

√

2

x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}

x=2a−b±b2−4ac​​

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

2

+

5

−

2

=

0

x^{2}+5x-2=0

x2+5x−2=0

=

1

a={\color{#c92786}{1}}

a=1

=

5

b={\color{#e8710a}{5}}

b=5

=

−

2

c={\color{#129eaf}{-2}}

c=−2

=

−

5

±

5

2

−

4

⋅

1

(

−

2

)

√

2

⋅

1

Step-by-step explanation:

this should help

Answer:

nsjdjdnajakla ,bxn. dnsksksvhdjeke dkekdkbdjdls d

The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees

The diagram is not shown; however, the question can still be answered.

The given angles are:

[tex]\theta_1 = 74.0^o[/tex]

[tex]\theta_2 = 66.0^o[/tex]

Represent the third angle as [tex]\theta_3[/tex]

The helicopter and the 2 VORs form a triangle.

So, we make use of the following theorem to calculate the third angle

[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle

Substitute known values

[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]

[tex]140.0^o + \theta_3= 180^o[/tex]

Collect like terms

[tex]\theta_3= 180 -140.0^o[/tex]

[tex]\theta_3= 40^o[/tex]

Hence, the third angle is 40 degrees.

Learn more about angles in a triangle at:

https://brainly.com/question/14780489

= 2025

When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)

For this, you divide the given lengths using the numbers that divides all through.

I have added an image to this answer. Go through it for more explanation

Answer: About 63 in²

Step-by-step explanation:

Area of circle = π · r²

Area of large pizza:

[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]

Area of small pizza:

[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]

Difference in area:

[tex]113.04-50.24=62.8[/tex]

Answer:

Mark Brainliest please

The answer is 1

Step-by-step explanation:

(1 — x^ m-n) ^-1 + (1- x ^n-m)^ -1

1/[1-x^(m-n)] + 1/[1-x^(n-m)]

1/[1-x^m × x^(-n)] + 1/[1-x^n × x^(-m)]

x^n/(x^n - x^m) + x^m/(x^m - x^n)

x^n/(x^n - x^m) - x^m/(x^n - x^m)

Now taking the LCM here, we get

(x^n - x^m)/(x^n - x^m)

Answer: Always equal to

Step-by-step explanation:

A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means.

Based on the options given, it should be noted that SS (Treatment) in the one-way ANOVA model is always equal to the SS (Treatment) in the randomized block design ANOVA model.

Answer:

7

Step-by-step explanation:

i had it

Answer:

Distance = 7 7/9 Km

Step-by-step explanation:

Given the following data;

Distance = 2⅔ = 8/3 Km

Time = ⅗ hour

First of all, we would find her speed;

Speed = distance/time

Speed = (8/3)/(3/5)

Speed = 8/3 * 5/3

Speed = 40/9 km/h

Next, we would find the distance covered when time = 1¾ hours

Distance = speed * time

Distance = 40/9 * 1¾

Distance = 40/9 * 7/4

Distance = 10/9 * 7

Distance = 70/9

Distance = 7 7/9 Km

Answer:

21.38 minutes

Step-by-step explanation:

the total number served = 101

teh number of hours that is spent in serving from 11.30 to 1.30 = 2 hours

Lq = average number of those that are in line = 18 customers

from here we are to find the flow rate

= [tex]\frac{total served}{service hour}[/tex]

= 101/2 = 50.5

the average time in waiting =

Lq/flow rate

= 18/50.5

= 0.3564 hours

convert to minutes = 0.3564 * 60 minutes

= 21.38 minutes

Answer:

35/37

Step-by-step explanation:

sin(B)=(AC)/(AB) = 35/37

Answer:

[tex]2^{3} * 3 * 5[/tex]

Step-by-step explanation:

===========================================================

Explanation:

All direct variation equations are of the form y = kx, for some constant k.

We know that y = -8 and x = 4 pair up together. Let's use these two values to find k

y = kx

-8 = k*4

-8/4 = k

-2 = k

k = -2

Therefore, we go from y = kx to y = -2x

We can then find y when x = -4

y = -2x

y = -2*(-4)

y = 8

Answer:

y∝x

y=kx

k=y/x

by putting values

k=-8/4

k= -2

now ,if x= -4

as, y=kx

hence, y= (-2)(-4)

y=8

Step-by-step explanation:

Answer:

the since ratio is 5/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

8/5 = 16/10 = 24/15

8:5 = 16:10 = 24:15

Answer:

x = 57

y = 57

Step-by-step explanation:

because of the two parallel lines :

41+y+8+74 = 180 add like terms

y + 123 = 180 subtract 123 from both sides

y = 57

x - 3 + 41 + y + 8 = 180 because they make a straight line

x + y + 46 = 180

x + 57 + 46 = 180

x + 123 = 180 subtract 123 from both sides

x = 57

Answer:

You can expect to make $250.

Step-by-step explanation:

Possible outcomes:

For the pair of dice:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

So 36 total outcomes.

Probability of the second number rolled being the same as the first number rolled:

6 outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

Out of 36, thus:

[tex]p = \frac{6}{36} = \frac{1}{6}[/tex]

Expected value of 1 game:

1/6 probability of earning $25.

5/6 probability of losing $2.

Thus:

[tex]E = 25\frac{1}{6} - 2\frac{5}{6} = \frac{25 - 10}{6} = 2.5[/tex]

100 games:

100*2.5 = 250

You can expect to make $250.

9514 1404 393

Answer:

  3/2

Step-by-step explanation:

Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.

  [tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]

Answer:

r=24

s=21

Step-by-step explanation:

I use proportion of 2 to 3

I multiply 16 and 3/2 to get r

r=24

I multiply 14 and 3/2 to get s

s=21

Step-by-step explanation:

When adding two fractions with different bases (bottom numbers), we can use this function:

[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]

So, to apply this to the given question:

[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]

= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]

From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.

= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]

= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]

= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]

= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]

Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.

= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

Answer:

A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

Answer:

6/25

Step-by-step explanation:

P(have belief) =76/100 = 19/25

P (does not have belief) = 1-19/25 = 6/25

Answer:

√202

Step-by-step explanation:

since it's the hypotenuse you are required to find

x²=11²+9²

x²=121+81

√x²=√202

x=√202

I hope this helps

Answer:

x²-36 and (x-6)(x+6)

9x-1 and(3x-1)(3x+1)

4x² -16 and 4(x-2)(x+2)

Step-by-step explanation:

when you multiply(x+6)(x-6)

you get x²-36,this is known as difference of two squares ie (a+b)(a-b)=(a²-b²)=0

x(x-6)+6(x-6)

x²-6x+6x-36

x² -36

the second the same explanation as the first

for the third, multiply (x+2)(x-2) it will give x²-4

then multiply this by 4 which is = 4x² - 16

Step-by-step explanation:

Step-by-step explanation:

Measure of Angle 1 is 115 due to corresponding angles postulate

Measure of Angle 2 is 65 is linear pair postulate.

9514 1404 393

Answer:

  c.  about the origin

Step-by-step explanation:

The function is odd: replacing x with -x gives the negative of the function value:

  f(-x) = -f(x)

Odd functions are symmetrical about the origin.